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Equilibrium - BUGFIX - Make the magnetic-axis search robust to an unreliable psi-spline Hessian - #444
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Equilibrium - BUGFIX - Make the magnetic-axis search robust to an unreliable psi-spline Hessian#444d-burg wants to merge 1 commit into
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…eliable psi-spline Hessian Two failure modes of `direct_position!` on otherwise healthy geqdsks, both caused by the 2-D psi spline's second derivatives near the axis (dB_z/dR wanders between ~5 and ~0 within a few cells, so the Hessian goes near-singular or indefinite): 1. "Jacobian matrix is singular" -- one bad iterate sent the undamped Newton step across the whole box, into a region where det J underflowed. 2. "Failed to find magnetic axis after 200 iterations" -- Newton cycled between two points either side of the axis on an indefinite Hessian. Fix, in two stages that leave the converging path untouched: * Cap each Newton step at one midplane-march step. Inactive for well-behaved iterations (their steps are < dr/2); it only keeps a bad iterate inside the axis neighbourhood until the Hessian recovers. A singular Hessian now returns "not converged" instead of erroring. * If Newton does not converge, locate the axis with first derivatives only: B_z changes sign across the axis along the midplane and B_r along a column, so four alternating 1-D bisections (80 iterations each, widening bracket in Z) converge to grad(psi) = 0 without touching the spline's second derivatives. Newton is retried from that point; if it still fails, the bisection point is used as the axis (it is a converged zero of the first derivatives) with an @info message instead of an error. Healthy equilibria never enter the fallback, so their results are bit-identical (regression harness: diiid_n1 47/47, diiid_slayer_n1 15/15, efit_fixedbdy_separatrix 5/5 unchanged vs 349a0c2). Two 257x257 TJ circular geqdsks reproducing each failure mode are added as fixtures with a test that both now locate the axis where the midplane B_z crossing says it is, and that a healthy geqdsk takes the plain Newton path. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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Release note
Reading some perfectly good geqdsks (seen on 257×257 TJ circular files, two of an 81-point β scan) used to abort with
Jacobian matrix is singular near (…)orFailed to find magnetic axis after 200 iterations. The cause is the 2-D ψ spline's second derivatives near the axis, which on these files are unreliable (∂B_z/∂R wanders between ~5 and ~0 over a few cells, so the Newton Hessian goes near-singular or indefinite). The axis search now caps each Newton step at one midplane-march step, and if Newton still fails, falls back to first-derivative bisection (B_z along the midplane, B_r along a column) before retrying Newton from there. Equilibria the old code handled never enter the fallback and are bit-identical.Regression report
regress --cases diiid_n1,diiid_slayer_n1,efit_fixedbdy_separatrix --refs 349a0c262,local(349a0c2 = thedeveloptip this branch is based on). 67/67 quantities unchanged.Notes for reviewers
TJ_circular_axis_newton_regression.geqdskfixture (singular Jacobian) is fixed by the step cap alone — capped Newton converges on its own. TheTJ_circular_axis_newton_cycling.geqdskfixture (indefinite Hessian, Newton cycles) needs the bisection stage. The test asserts which path each file takes via the@infomessage, and that a healthy geqdsk (CHEASE_test_data/EQDSK_COCOS_02) takes the plain Newton path.diiid_n1energies by 0.02% and SLAYER γ by 0.2%. Newton-first with bisection as the fallback leaves the converging path untouched, hence the clean harness.error; the only remaining hard error indirect_position!is the midplane march failing to find a B_z sign change, which is a genuinely broken file.🤖 Generated with Claude Code